Some ideas you may not have tried for the baby:
Maybe he's getting too much air, or too little.
Check to make sure sun isn't getting in his eyes.
Try running your errands at different times of the day.
Try vibrating the car seat with your hand.
Try having the non-driving adult sit in the back next to him.
For the distracted driving part, the best thing I've found is not to try to block everything out, but to intentionally dedicate a very rote part of your brain to the distraction. Try singing or talking to the baby, but something very repetitious you don't have to think about. Your brain sort of says, "Oh, he knows about the baby screaming so I don't have to keep interrupting him." Then focus on keeping your conscious attention on the road.